{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Heat Flow\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Heat_Flow.ipynb)\n",
    "\n",
    "This example simulates heat flow through metal bars surrounded by an insulator.\n",
    "The conductivity of the bars is much higher than the other material."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip --quiet install phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by defining the domain and bar geometries. For the bars, we set the conductivity close to 1 while the rest has a conducitivity of 0.01."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "domain = Box(x=10, y=5)\n",
    "boundary = {'x-': 1, 'x+': ZERO_GRADIENT, 'y': PERIODIC}\n",
    "bars = union(Box(x=(0, 10), y=(2, 3)), Box(x=(4.5, 5.5), y=(1, 4)))\n",
    "conductivity = CenteredGrid(bars, ZERO_GRADIENT, domain, x=100, y=50) + .01\n",
    "\n",
    "plot({\"Geometry\": [domain, bars], \"Conductivity grid\": conductivity}, overlay='list')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use implicit diffusion here. Explicit diffusion works the same way but becomes unstable for large $\\Delta t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(t, dt):\n",
    "    return diffuse.implicit(t, conductivity, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fc05351cb5e44135846aaabd842ba9de",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t0 = CenteredGrid(0, boundary, domain, x=100, y=50)\n",
    "t_trj = iterate(step, batch(time=100), t0, dt=1, range=trange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x2409db19490>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(t_trj, animate='time')"
   ]
  }
 ],
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   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}
